RANDOM NUMBER GENERATOR AND VIRTUAL REEL

For many decades after reel slot machines were invented, the number of symbols on each reel coupled with the payoff on each winner determined the game’s payback percentage.
That’s no longer the case. The random number generator and virtual reel have led to machines where the real game is being played internally, in the machine’s software. When the random numbers have been selected, the game programming tells the reels which symbols to display.

ABOUT RANDOM NUMBERS

It’s said that nothing in the universe above quantum level is truly random, but random number generators are close enough that players can’t discern any repeating patterns, and the long-term percentages are those you would expect from randomly occurring outcomes. Here are a few key points about the RNG:

• RNGs use algorithms to calculate their numbers.
• RNGs are very fast, generating dozens and sometimes hundreds of random numbers per second.
• The RNG keeps running even when the machine is not being played.
• The only function of the RNG is to generate random numbers. It doesn’t know how those numbers are used.
• The RNG works with a full set of numbers on every spin, so all results are possible on every spin.

How many random numbers are used and how they are mapped onto symbols differs from game to game. So do the entry points to start the next calculation. With more sophisticated RNGs, hitting the “Bet One Coin” button, the “Max Bet” button or pulling the handle could start the algorithm from different points. Because the RNG works so fast, if you pause slightly before your next play or stop for a few seconds to order a beverage or chat with a neighbor, your result will be different than if you kept at the same pace. That doesn’t mean your result will necessarily be better or worse, just different.

If you leave a machine and someone else takes your place and hits the jackpot, that doesn’t mean you’d have won if you’d stayed. The RNG would be at a different point in its calculations.

ABOUT THE VIRTUAL REEL

The virtual reel makes it possible to have a much larger range of outcomes than if odds were determined by the number of symbols and spaces on a mechanical reel Mechanical reels must fit inside a machine’s casing. You can increase a reel’s size from 10 symbols and 10 spaces to 20 and 20, 30 and 30 and so on up to a point, but if you want to drive odds that make a really big jackpot possible, you need more combinations than physical reels alone can handle. Mapping symbols and spaces onto a virtual reel dramatically increases the number of possible combinations.

Let’s keep the arithmetic simple, and say you have a reel with 10 symbols and 10 spaces. The symbols can be the same as the example in Chapter 2-1: Each reel has one 7, two bars, three cherries and four watermelons.

But instead, let’s map all those symbols and spaces onto a virtual reel, so there are 50 stops on each reel:

A FEW THINGS OF NOTE:

In this example, each like symbol was given the same number of stops on the virtual reel. That doesn’t have to be the case. Cherry No. 1 could be given three stops and Cherry No. 2 six stops, or any other number, if that’s what fits the desired odds of the game. Mapping does not have to be identical for each reel. Cherry No. 1 could have three random numbers on reel No. 1, four on reel No. 2 and five on reel No. 3, if that led to the desired odds. On mechanical-reel machines today, the spaces between symbols also are stops. Symbols alone were counted here to simplify the arithmetic for the same of example.

 

Now let’s compare what the virtual reel does to the number of combinations, compared to the physical reels alone.

With odds determined by the physical reel, the chances of lining up the rarest combination, 7-7-7, are 1 in 1,000, so the jackpot can’t be very large. Even if you keep paybacks very small on other three-symbol combinations, it would be difficult to have a top jackpot of more than a couple of hundred coins. By mapping those symbols onto this simplified virtual reel, the jackpot chances become 1 in 125,000. Now the jackpot can run into thousands of coins, and there’s a lot more room for paybacks on other symbols. Let’s use physical reels and virtual reels to make up pay tables that are identical, except with the jackpot set high enough to bring the total return to 90 percent:

Both those games have odds that would lead to a 90 percent return, but letting the number of symbols on the physical reel dictate the odds leads to a jackpot of not quite 300 coins while using the virtual reel enables jackpot of more than 25,000 coins.

Everything’s easily adjustable with so many possibilities. Game designers can give you a less volatile game by making the jackpot smaller and increase paybacks on lesser winners. There’s not the same kind of wiggle room when you’re dealing with only 1,000 possible combinations.

• combination of a random number generator and a virtual reel determine what symbols and spaces you see on a slot with mechanical reels.
• The random number generator operates continuously, even when a machine is not being played, and any change in your timing will lead to a different result.
• The virtual reel can make a physical reel behave as if it has many more symbols than it really does, and leads to more possible combinations.
• The increase in the number of combinations enables bigger jackpots and more variation in payoffs.

HIT FREQUENCY VS. PAYBACK PERCENTAGE

Winning the most often doesn’t always translate into winning the most money. There are two separate concepts:

• Hit frequency is the proportion of spins that pay money to players.
• Payback percentage is the proportion of wagers returned to players as winnings.

Let’s start by considering two games with identical pay tables, but different hit frequencies. These are not real games; it’s just an example set up to make the arithmetic that follows easy. Reel stops include blank spaces as well as symbols, but only three of the same symbol form a winning combination. Odds are set so there are 10,000 possible combinations, so what’s listed in this table are the number three-symbol possibilities per 10,000 spins:

We can tell several things from the chart above:

• Of 10,000 combinations, Game A has 1,336 winners to only 1,005 on Game A.
• The 1,336 Game B winners give it a 13.36 percent hit percentage, to 10.05 percent on Game A.
• Both the hit frequencies and paybacks per win are the same on 7s, bars and cherries.
• The 331 extra melon winners give Game B both a higher hit frequency and higher payback percentage.

Per 10,000 coins wagered, each game pays 1,000 on 7s, 3,500 on bars and 3,000 on cherries, for a total of 7,500. But Game A pays 1,338 on melons, and game B pays 2,000. That makes the total return 8,838 on Game A, giving it an 88.8 percent payback percentage. Game B has a total payback of 9,500 coins for a 95 percent payback percentage.

If these two games were sitting side-by side in the casino, they would appear to be identical. Winning combinations and their paybacks would be displayed, and those are the same. Players would not be able to tell one machine had a higher hit frequency and payback percentage.

ADJUSTING THE PAY TABLE

What if a slots game designer wanted a machine with Game A’s hit frequency, but Game B’s payback percentage, or Game B’s hit frequency but Game A’s payback percentage? One route is by adjusting the pay table.

• The hit frequencies are still 13.36 percent on Game B and 10.5 percent on Game B.
• The payback on cherries has been changed to 120 on Game A, and down from 100 to 80 on Game B.
• Game B still has a higher hit frequency.
• Game A now has a higher payback percentage.

The larger payoffs on cherries are enough to bring Game A up to a 95.38 percent payback percentage, just a fraction more than Game B paid in the first example. Game B is now down to 88 percent, a fraction less than Game A paid earlier. So here, the game with the higher hit frequency is actually the lower payer.

WHAT YOU SEE VS. WHAT YOU GET

In the above example, it looks like you can tell which is the higher payer, because Game A both pays more on cherries and has a higher payback percentage. Can a glance at the pay table tell you which game is a higher payer?

The answer to that is no, a look at the pay table can be misleading. Let’s try one more example, in which one game pays more on every winning combination. Once again, we’re using an example with 10,000 possible reel combinations.

From the outside, Game A looks like a much higher payer, paying 1,500 vs. 1,000 for Game B on three 7s, 150 vs. 100 on 100 on bars, 20 vs. 10 on cherries and 2 vs. 1 on melons.

But internally, out of your view, the hit frequencies also have been changed. Game A now has a hit frequency of only 5.76 percent, while Game B has been increased to 25.31 percent.

Let’s look at what that does to the overall payback, adjusting for the number of winners for each three-symbol combo:

 

Such a large number of low-paying spins means Game B will have low volatility, which has the effect of extending your play.

Games with such a large difference in hit frequency but such a small difference in payback percentage were used to show you the kind of leeway game designers have. If 2,050 melon combinations were used instead of 2,200, the games would have identical payback percentages, but would be vastly different playing experiences.

In that case, you would have a better chance at winning big at Game A, but a better chance at extended playing time at Game B. Real games are more complex than these examples, but offer the same kinds of different playing experiences.

On real three-reel mechanical slot games, hit frequencies as low as 5.76 percent and as high as 25.31 percent are rare. Real three-reel, single-payline games have hit frequencies that cluster between about 9 and 13 percent. Games with more paylines have higher hit frequencies.

The examples above are to illustrate principles. Real mechanical slots and their math are more complex. Three-reel games usually have more than four symbols, opening more possibilities, and game programmers aren’t confined to using number sets that yield 10,000 combinations – in fact, on big jackpot slots games, the number sets are much, much larger.

Here are a few additional factors that add complexity, texture and fun to the mechanical-reel portion of modern slot floors:

• Many newer three-reel slots have more than one payline.
• Games with more than three mechanical reels have a niche in casinos, with five reels often used.
• Many three-reel games today also incorporate bonus events.

Games with multiple paylines open more possibilities and add complexity to the calculations. Three lines across the screen plus two diagonals take a game to five lines, and more lines can be created with Vs and zigzags, just like on video slots. In recent years, game manufacturers have produced three-reel mechanical games with as many as 27 paylines. Bonus events also add complexity to calculation. A diminishing number of games put all the focus omn the spinning reels. However, many three-reel games incorporate free spins, bonus wheels on top of the games, or secondary video screens to create a hybrid mechanical-video game. Any bonus payouts have to be accounted for in calculating the game’s overall return.

• Higher hit frequencies don’t always bring higher overall returns.
• A game that looks like a high-payer to a player could actually be a lower-paying game than one with a lower pay table.
• Game designers and programmers use a combination of hit frequency and payback per win to get to a final payback percentage.
• Additional factors in modern mechanical slots include multiple paylines, using five reels instead of three and incorporating bonus events into the games.